Explanation The region R connects the points ( 0 , 1 ) , ( 0 , − 1 ) , ( − 1 , 0 ) and ( 0 , 1 ) . This region is in the shape of a diamond. Therefore, the radius of the circle is ( y + 1 ) in the lower half of the x − y − plane and the radius of the circle is ( 1 − y ) in theupper half of the x − y − plane...

4th Edition

ISBN: 9781319050733

Author: Rogawski

Publisher: MAC HIGHER

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Chapter 6.2, Problem 15E

To determine

To find the volume of the solid whose base is the region $| x | + | y | \leq 1$ and whose vertical cross sections perpendicular to the $y -$ axis are semicircles (with diameter along the base).

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Chapter 6.2, Problem 14E

Chapter 6.2, Problem 16E

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(3) (20 points) Let F(x, y, z) = (y, z, x²z). Define E = {(x, y, z) | x² + y² ≤ z ≤ 1, x ≤ 0}. (a) (2 points) Calculate the divergence V. F. (b) (4 points) Let D = {(x, y) | x² + y² ≤ 1, x ≤ 0} Without calculation, show that the triple integral √ (V · F) dV = √ 2²(1. = x²(1 − x² - y²) dA. E

(2) (22 points) Let F(x, y, z) = (x sin y, cos y, ―xy). (a) (2 points) Calculate V. F. (b) (6 points) Given a vector field is everywhere defined with V G₁(x, y, z) = * G2(x, y, z) = − G3(x, y, z) = 0. 0 0 F(x, y, z) = (F₁(x, y, z), F₂(x, y, z), F(x, y, z)) that F = 0, let G = (G1, G2, G3) where F₂(x, y, y, t) dt - √ F³(x, t, 0) dt, * F1(x, y, t) dt, t) dt - √ F Calculate G for the vector field F(x, y, z) = (x sin y, cos y, -xy).

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Chapter 6 Solutions

CALCULUS (CLOTH)

Ch. 6.1 - Prob. 1PQ Ch. 6.1 - Prob. 2PQ Ch. 6.1 - Prob. 3PQ Ch. 6.1 - Prob. 4PQ Ch. 6.1 - Prob. 5PQ Ch. 6.1 - Prob. 6PQ Ch. 6.1 - Prob. 1E Ch. 6.1 - Prob. 2E Ch. 6.1 - Prob. 3E Ch. 6.1 - Prob. 4E

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To find the volume of the solid whose base is the region | x | + | y | ≤ 1 and whose vertical cross sections perpendicular to the y − axis are semicircles (with diameter along the base).

Solution Summary: The author determines the volume of the solid whose base is the region x | + | y 1 and its vertical cross sections are semicircles (with diameter along the base).

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To find the volume of the solid whose base is the region $| x | + | y | \leq 1$ and whose vertical cross sections perpendicular to the $y -$ axis are semicircles (with diameter along the base).

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Chapter 6 Solutions

To find the volume of the solid whose base is the region | x | + | y | ≤ 1 and whose vertical cross sections perpendicular to the y − axis are semicircles (with diameter along the base).

Solution Summary: The author determines the volume of the solid whose base is the region x | + | y 1 and its vertical cross sections are semicircles (with diameter along the base).

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To find the volume of the solid whose base is the region |x|+|y|≤1 and whose vertical cross sections perpendicular to the y− axis are semicircles (with diameter along the base).

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Chapter 6 Solutions

To find the volume of the solid whose base is the region $| x | + | y | \leq 1$ and whose vertical cross sections perpendicular to the $y -$ axis are semicircles (with diameter along the base).